A newborn is literally a baby animal (including us human animals) who was born in the past month. Figuratively, newborn describes anything recently born or created, like a newborn interest in vocabulary.
Little babies are newborns until they're a month old — four weeks is the official human newborn cut-off age. Then they’re just regular ol’ babies. Other things can be newborn as long as they’re brand new — a newborn restaurant was opened recently, a newborn celebrity might be 18 but she just got famous. You could have a newborn fear if you recently became scared of something. Most newborns are not scary, though. (Unless you’re babysitting one.)